copyright © 2009 pearson education, inc. chapter 9 section 4 - slide 1 and

Copyright © 2009 Pearson Education, Inc. Chapter 9 Section 4 - Slide 1

AND

Chapter 9 Section 4 - Slide 2Copyright © 2009 Pearson Education, Inc.

Chapter 9

Geometry


WHAT YOU WILL LEARN

• Points, lines, planes, and angles• Polygons, similar figures, and

congruent figures• Perimeter and area• Pythagorean theorem• Circles• Volume


Section 4

Volume and Surface Area


Volume

Volume is the measure of the capacity of a figure.

It is the amount of material you can put inside a three-dimensional figure.

Surface area is sum of the areas of the surfaces of a three-dimensional figure.

It refers to the total area that is on the outside surface of the figure.


r

Volume Formulas

Sphere

Cone

V = r2hCylinder

V = s3Cube

V = lwhRectangular Solid

DiagramFormulaFigure

213V r h

343V r

l

h

w

s

s

s

h

h

r


r

Surface Area Formulas

Sphere

Cone

SA = 2rh + 2r2Cylinder

SA= 6s2Cube

SA = 2lw + 2wh +2lhRectangular Solid

DiagramFormulaFigure

SA r2

r r2

h2

SA 4r 2

l

h

w

s

s

s

h

r

h

r


Mr. Stoller needs to order potting soil for his horticulture class. The class is going to plant seeds in rectangular planters that are 12 inches long, 8 inches wide and 3 inches deep. If the class is going to fill 500 planters, how many cubic inches of soil are needed? How many cubic feet is this?

Example

12

3

8


Example (continued)

We need to find the volume of one planter.

Soil for 500 planters would be

500(288) = 144,000 cubic inches The number of cube feet

V lwh

V 12(8)(3)

V 288 in.3

33 3 3

3

1 ft 144,000144,000 in ft 83.33 ft

1728 in 1728

æ ö= = =ç ÷è ø


Polyhedron

A polyhedron is a closed surface formed by the union of polygonal regions.


Euler’s Polyhedron Formula

Number of vertices number of edges + number of faces = 2

Example: A certain polyhedron has 12 edges and 6 faces. Determine the number of vertices for this polyhedron.

# of vertices # of edges + # of faces = 2

There are 8 vertices.

12 6 2

6 2

8

x

x

x


Volume of a Prism A prism is a polyhedron whose bases are

congruent and whose sides are parallelograms. V = Bh, where B is the area of the base and h is

the height. Example: Find the volume of the figure.

Area of one triangle. Find the volume.

8 m

6 m

4 m

12

12

2

(6)(4)

12 m

A bh

A

A

3

12(8)

96 m

V Bh

V

V


Volume of a Pyramid

A pyramid is a polyhedron with one base, all of whose faces intersect at a common vertex.

where B is the area of the base and h is the height.

Example: Find the volume of the pyramid.Base area = 122 = 144

13V Bh

12 m

12 m

18 m

13

13

3

(144)(18)

864 m

V Bh

V

V

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